A Subtle Symmetry of Lebesgue's Measure


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Uludag M. , Ayral H.

JOURNAL OF THEORETICAL PROBABILITY, cilt.32, ss.527-540, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 32 Konu: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s10959-017-0804-y
  • Dergi Adı: JOURNAL OF THEORETICAL PROBABILITY
  • Sayfa Sayıları: ss.527-540

Özet

We represent the Lebesgue measure on the unit interval as a boundary measure of the Farey tree and show that this representation has a certain symmetry related to the tree automorphism induced by Dyer's outer automorphism of the group PGL(2,Z). Our approach gives rise to three new measures on the unit interval which are possibly of arithmetic significance.